Multiple Approaches
LTSN MathsTEAM Project Maths for Engineering and Science
Using Technology to Teach Mathematics
to First Year Engineers
Neil Challis and Harry Gretton ■ School of Science and Mathematics ■ Sheffield Hallam
University
Abstract
This case study reports on the approach at one institution to helping first year engineering students to acquire the
mathematical skills they need. The approach involves a range of support mechanisms, and the concerted use of technology
as well as paper and pencil methods. Changes in curriculum, pedagogy and indeed assessment style have all proven
necessary.
Level of Material: First Year
The Execution
Using Technology to Teach Mathematics to First Year Engineers
Mathematical topics are treated according to ‘SONG’ – a
combination of Symbolic, Oral, Numerical and Graphical
approaches – broader than the traditional mainly symbolic
approach, and in the same vein as with the Calculus Reform
movement in the USA. Students are encouraged to engage in
doing mathematics, and to exploit a range of technology
throughout – graphics calculator, spreadsheet, Derive, pencil,
etc. The rich interplay of graphic, symbolic and numerical
approaches is emphasised. Technology empowers students to
check their own solutions. Sometimes, mathematical ideas are
introduced via modelling of an engineering situation. The ‘Oral’
refers to communicating mathematical ideas, formulating
engineering problems and communicating the solution
appropriately. Some relevant modelling case study assessments
are thus used – with students encouraged to take full ownership
of the problem, with some marks being given for demonstrating
various key skills. Examples appear in the references.
Pre-requisite Knowledge
There is a widely recognised problem with what can be
assumed as pre-requisite knowledge and skills for engineering
students newly arriving at university. The problem arises from a
complicated set of circumstances including: changes in preuniversity mathematics, the diversity of backgrounds of students
entering university, the need for development of curriculum (and
staff) to make university expectations realistic and the impact of
technology on what is really required. We hope for a certain
level of numeracy, including sensible use of a calculator, a
certain fluency in algebraic techniques, and some previous
acquaintance with the ideas of the calculus. Many students in
the group do not have A Level Mathematics, so we are
frequently disappointed. It is a major task of the module to get
the students to revisit and enhance previously encountered
topics as well as moving onto new topics. The diagnostic plays
a role here. We do not use the word remedial because of the
possible stigma – each student revisits topics according to
need.
www.mathcentre.ac.uk
Given the diverse intake, the module must strike a balance
between, on the one hand getting students to cover the ground
as laid out in the module document and on the other allowing
each person to start from a position which makes sense to them
individually. The curriculum is challenged by technology anyway
– for instance how much of the traditional range of paper and
pencil integration techniques must now be covered on paper
before we will allow our students to feel comfortable with widely
available CAS systems? We hope that students will benefit from
a fresh approach to topics with which they may not have been
entirely comfortable previously and we believe that motivation
and interest are important alongside pre-requisite knowledge.
How Are Students With
Different Mathematical
Backgrounds Supported?
The whole module is predicated on a diverse intake, but there
are additional measures in place. There is a range of support
materials on paper and on-line, covering both module material
and surrounding or prior topics. The initial diagnostic can set an
agenda which can be supported through standard tutorials, the
drop-in Maths Help, extra targeted tutorials and additional
credit-bearing modules. Each worksheet has a range of
problems and activities, with the aim of stretching the more
advanced students, while giving all something in which to
engage.
What Support Was Needed?
Key staff participate in, contribute to and learn from international
conferences and national events, to exchange ideas and
practice and to widen their perspective. Continuing funding and
time is needed for this. In fact time for reflection and to interact
with the academic community is the main resource needed.
Tutorial staff and engineering staff affected by changing student
skills have participated in local developmental events, for
example, giving the opportunity to explore the implications of the
technology. IT support is required to load, maintain and update
software.
© The authors 2003
The Barriers
Some staff have displayed a certain resistance to change,
although when they explore and reflect on the philosophy and
approach, the reservations often focus in on an unease about
assessment. There are various examples of this: the use of
calculators in examinations and the possibilities for “hiding” facts
in the memory (but should we be testing memory?); or the value
or otherwise of radical ideas such as learning diaries, which
may enhance key skills and encourage more thoughtful
learning, but which from a narrow focus may be seen as a
distraction. Some staff found the loss of control – with students
knowing the technology better than them – a difficulty.
The main point is to reflect on the approach and how it might
make a contribution within each person’s context. Some might
feel able to go further than others. But our experience is that if
you wait for all to agree before you try something innovative
then you will never change. To learn from and improve an
innovative approach you need to try things and gain experience.
Computers have been with us (and our students) substantially
and increasingly for 40 years, and now real power is widely
available and even hand-held, then we must deal with it. It is
possible to experiment incrementally to some extent, but there
comes a point where, for instance, someone has to propose
and decide that graphics calculators are allowed in
examinations.
Quality Assurance
Module feedback forms covering all aspects of Teaching
Learning and Assessment (TLA) give scores much in line with
other modules.
Other Recommendations
Share ideas and materials, and be honest about both
successes and difficulties.
The most important enabler is enthusiasm amongst staff. This
has been an interesting experience of innovation, with the ideas
being spread from a small group and adopted and adapted
progressively and variously amongst both mathematics and
engineering staff as they have had time to gain experience and
to reflect. Small successes help things along, such as a student
finding a novel way to solve a real engineering problem using
technology, or an engineer seeing a way of integrating the new
approach into a laboratory. It is important to be willing to discuss
the approach openly with students, and we believe this
reflection is an important part of learning.
■
Put key handouts on both paper and as electronic files, but
have a variety of other materials.
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Don’t imagine any one thing – diagnostic, computer based
learning, virtual environments, technology, drill and kill …will solve all problems. The one universal thing is that
students need human contact to help them face up to their
mathematical problems.
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Present a range of approaches both technological and
traditional and take account of diverse students with varying
learning styles. You can bring them all to water, but some
prefer it flavoured!
Evidence of Success
■
Come and talk to us if you are interested!
We can only report qualitatively: to report on any improvement
or otherwise in exam performance is not helpful as the nature of
the assessment is changed when students are empowered by
technology. As with all approaches, some students fare better
than others – and it is best with those who engage fully. These
latter have produced some remarkable work. Evaluation through
quality systems, questionnaire, learning diary, and a more
concerted set of group interviews give the diversity of views
which might be expected. We do not claim to have the answer,
but we have embarked on a very interesting learning process.
References
“Expressive and explicit CAS – is it enough?”, International
Journal of Computer Algebra in Mathematics Education, 9(2),
p155, Challis, N., Gretton, H., (2002).
“Diagnosing mathematical needs and following them up”, in
Manfred Borovcnik, Hermann Kautschitsch (eds): Technology in
Mathematics Teaching. Proceedings of the ICTMT 5 in
Klagenfurt 2001, Schriftenreihe Didaktik der Mathematik v. 25.
öbv&hpt, Vienna 2002, Challis, N., Gretton, H., Robinson, M.,
Wan ,S., (2001).
“Technology, key skills and the engineering mathematics
curriculum”, Proc. IMA conference on Mathematical Education
of Engineers, (IMA), pp 145-150, Challis, N., and Gretton, H.,
(1997).
“What is doing mathematics now that technology is here?”, in
Yang, W-C et al (eds), Proceedings of the Fifth Asian
Technology Conference in Mathematics, ATCM Inc, USA,
Gretton, H., and Challis, N., (2000).
www.mathcentre.ac.uk
© The authors 2003
Using Technology to Teach Mathematics to First Year Engineers
■
The Enablers
LTSN MathsTEAM Project Maths for Engineering and Science
Students have preconceptions of mathematics and a broader
approach which requires them to engage fully can provide a
challenge for some. Some say, “I don’t like to use technology
until I understand the basics”, but upon investigation it is not
clear what “the basics” are. Some say “technology is just
pressing buttons”, failing to understand the challenging
message that technology can help focus on the mathematical
idea (although some do want to be taught which buttons to
push!). Many students do not recognise the contribution this
approach to mathematics can make to key skills development
and tend to compartmentalise mathematics anyway.
How Can Other Academics
Reproduce This?